this is for holding javascript data
adam greenberg edited method.tex
about 10 years ago
Commit id: bc131ac19fea0f6d7facd433a117b3c63df7e9b0
deletions | additions
diff --git a/method.tex b/method.tex
index 5cf1a92..edf314a 100644
--- a/method.tex
+++ b/method.tex
...
\subsection{Steepest Descent Routine}
A classical steepest descent routine (SDR) minimizes the weighted residuals between a model and data with Gaussian noise by determining the direction in parameter space in which the $\chi^2$ is decreasing fastest. Specifically, suppose one has a set of $m$ observables, $\vec{z}$ with weights $W$, and a model function $\vec{m}(\vec{x})$, where \vec{x} is an $n$-dimensional parameter vector. Assuming independent data points with Gaussian-distributed errors, the probability of the model matching the data is given by \[p(\vec{m}(\vec{x}) | \vec{z}) \propto p(\vec{z} | \vec{m}(\vec{x})) \propto \exp(
\frac{1}{2}\vec{R}^T \frac{-1}{2}\vec{R}^T W \vec{R})\]
where $\vec{R} = \vec{z} - \vec{m}(\vec{x})$